Commutative Algebra seminar
Speaker: Prof. R. V. Gurjar, TIFR Bombay *Retd.)
Host: Tony Puthenpurakal
Title: Singularities of plane curves
Time, day and date: 3:00:00 PM - 4:00:00 PM, Thursday, February 19
Venue: Ramanujan Hall
Abstract: We will consider reduced power series f(X,Y) over an algebraically closed field k of characteristic 0. Following topics about R=k[[X,Y]]/(f) will be discussed.
Algebraicity results of Artin, Hironaka-Rossi, Samuel, Basic intersection theory of place curves, Conductor ideal, Value semi-group of R, Gorenstein's result, Dedekind's Conductor Formula, Jung's formula connecting the Milnor number and conductor, Applications of Dedekind's formula. We will give Abhyankar's proofs of Dedekind and Gorenstein results. If time permits, Abhyankar-Moh result about generators of the value semi-group will be discussed.